Group testing was first proposed for blood tests, but soon found its way to many industrial applications. Combinatorial group testing studies the combinatorial aspect of the problem and is particularly related to many topics in combinatorics, computer science and operations research. Recently, the idea of combinatorial group testing has been applied to experimental designs, coding, multiaccess computer communication, clone library screening and other fields. This book is the first attempt to cover the theory and applications of combinatorial group testing in one place.

" Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers the spectra of rings chain conditions, dimension theory, and Jaffard rings fiber products group rings, semigroup rings, and graded rings class groups linear groups integer-valued polynomials rings of finite fractions big Cohen-Macaulay modules and much more "

Based on the fifth Mid-Atlantic Algebra Conference held recently at George Mason University, Fairfax, Virginia. Focuses on both the practical and theoretical aspects of computational algebra. Demonstrates specific computer packages, including the use of CREP to study the representation of theory for finite dimensional algebras and Axiom to study algebras of finite rank.

A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary stochastic analysis, Noncommutative Distributions: examines a theory of noncommutative distributions as irreducible unitary representations of groups of mappings from a manifold into a Lie group, with applications to gauge-field theories; describes the energy representation when the target Lie group G is compact; discusses representations of G-valued jet bundles when G is not necessarily compact; and supplies a synthesis of deep results on quasi-simple Lie algebras.;Providing over 200 bibliographic citations, drawings, tables, and equations, Noncommutative Distributions is intended for research mathematicians and theoretical and mathematical physicists studying current algebras, the representation theory of Lie groups, and quantum field theory, and graduate students in these disciplines.

About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the participants of these talks along with contributions from other veteran researchers who were unable to attend. These papers reflect many of the current topics in Abelian Groups, Commutative Algebra, Commutative Rings, Group Theory, Homological Algebra, Lie Algebras, and Module Theory. Accessible even to beginning mathematicians, many of these articles suggest problems and programs for future study. This volume is an outstanding addition to the literature and a valuable handbook for beginning as well as seasoned researchers in Algebra. about the editors H. PAT GOETERS completed his undergraduate studies in mathematics and computer science at Southern Connecticut State University and received his Ph.D. in 1984 from the University of Connecticut under the supervision of William J. Wickless. After spending one year in a post-doctoral position in Wesleyan University under the tutelage of James D. Reid, Goeters was invited for a tenure track position in Auburn University by Ulrich F. Albrecht. Soon afterwards, William Ullery and Overtoun Jenda were hired, and so began a lively Algebra group. OVERTOUN M. G. JENDA received his bachelor's degree in Mathematics from Chancellor College, the University of Malawi. He moved to the U.S. 1977 to pursue graduate studies at University of Kentucky, earning his Ph.D. in 1981 under the supervision of Professor Edgar Enochs. He then returned to Chancellor College, where he was a lecturer (assistant professor) for three years. He moved to the University of Botswana for another three-year stint as a lecturer before moving back to the University of Kentucky as a visi

Based on and enriched by the long-term teaching experience of the authors, this volume covers the major themes of mathematics in engineering and technical specialties. The book addresses the elements of linear algebra and analytic geometry, differential calculus of a function of one variable, and elements of higher algebra. On each theme the authors first present short theoretical overviews and then go on to give problems to be solved. The authors provide the solutions to some typical, relatively difficult problems and guidelines for solving them. The authors consider the development of the self-dependent thinking ability of students in the construction of problems and indicate which problems are relatively difficult. The book is geared so that some of the problems presented can be solved in class, and others are meant to be solved independently. An extensive, explanatory solution of at least one typical problem is included, with emphasis on applications, formulas, and rules. This volume is primarily addressed to advanced students of engineering and technical specialties as well as to engineers/technicians and instructors of mathematics. Key features: Presents the theoretical background necessary for solving problems, including definitions, rules, formulas, and theorems on the particular theme Provides an extended solution of at least one problem on every theme and guidelines for solving some difficult problems Selects problems for independent study as well as those for classroom time, taking into account the similarity of both sets of problems Differentiates relatively difficult problems from others for those who want to study mathematics more deeply Provides answers to the problems within the text rather than at the back of the book, enabling more direct verification of problem solutions Presents a selection of problems and solutions that are very interesting not only for the students but also for professor-teacher staff

This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry, finishing with a chapter on transformation groups; Part II is on quadratic forms and their geometry (Euclidean geometry), including a chapter on finite subgroups of 0 (2). Each of the 23 chapters concludes with a generous helping of exercises, and a selection of these have solutions at the end of the book. The chapters also contain many examples, both numerical worked examples (mostly in 2 and 3 dimensions), as well as examples which take some of the ideas further. Many of the chapters contain "complements" which develop more special topics, and which can be omitted on a first reading. The structure of the book is designed to allow as much flexibility as possible in designing a course, either by omitting whole chapters or by omitting the "complements" or specific examples.

In recent years, there has been a great deal of interest and activity in the general area of nonparametric smoothing in statistics. This monograph concentrates on the roughness penalty method and shows how this technique provides a unifying approach to a wide range of smoothing problems. The method allows parametric assumptions to be realized in regression problems, in those approached by generalized linear modelling, and in many other contexts.

The emphasis throughout is methodological rather than theoretical, and it concentrates on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. Some publicly available software is also discussed. The mathematical treatment is self-contained and depends mainly on simple linear algebra and calculus.

This monograph will be useful both as a reference work for research and applied statisticians and as a text for graduate students and other encountering the material for the first time.

This volume contains information offered at the international conference held in Curacao, Netherlands Antilles. It presents the latest developments in the most active areas of abelian groups, particularly in torsion-free abelian groups.;For both researchers and graduate students, it reflects the current status of abelian group theory.;Abelian Groups discusses: finite rank Butler groups; almost completely decomposable groups; Butler groups of infinite rank; equivalence theorems for torsion-free groups; cotorsion groups; endomorphism algebras; and interactions of set theory and abelian groups.;This volume contains contributions from international experts. It is aimed at algebraists and logicians, research mathematicians, and advanced graduate students in these disciplines.

Presenting the proceedings of a recently held conference in Provo, Utah, this reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum.;Detailing the integration of geometric, algebraic, analytic and arithmetic ideas, Number Theory with an Emphasis on the Markoff Spectrum contains refereed contributions on: general problems of diophantine approximation; quadratic forms and their connections with automorphic forms; the modular group and its subgroups; continued fractions; hyperbolic geometry; and the lower part of the Markoff spectrum.;Written by over 30 authorities in the field, this book should be a useful resource for research mathematicians in harmonic analysis, number theory algebra, geometry and probability and graduate students in these disciplines.

This volume collects presentations from the international workshop on local cohomology held in Guanajuato, Mexico, including expanded lecture notes of two minicourses on applications in equivariant topology and foundations of duality theory, and chapters on finiteness properties, D-modules, monomial ideals, combinatorial analysis, and related topics. Featuring selected papers from renowned experts around the world, Local Cohomology and Its Applications is a provocative reference for algebraists, topologists, and upper-level undergraduate and graduate students in these disciplines.

This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.

Multiple-Valued Logic Design: An Introduction explains the theory and applications of this increasingly important subject. Written in a clear and understandable style, the author develops the material in a skillful way. Without using a huge mathematical apparatus, he introduces the subject in a general form that includes the well-known binary logic as a special case. The book is further enhanced by more 200 explanatory diagrams and circuits, hardware and software applications with supporting PASCAL programming, and comprehensive exercises with even-numbered answers for every chapter.
Requiring introductory knowledge in Boolean algebra, 2-valued logic, or 2-valued switching theory, Multiple-Valued Logic Design: An Introduction is an ideal book for courses not only in logic design, but also in switching theory, nonclassical logic, and computer arithmetic. Computer scientists, mathematicians, and electronic engineers can also use the book as a basis for research into multiple-valued logic design.

This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.

Renewed interest in vector spaces and linear algebras has spurred the search for large algebraic structures composed of mathematical objects with special properties. Bringing together research that was otherwise scattered throughout the literature, Lineability: The Search for Linearity in Mathematics collects the main results on the conditions for the existence of large algebraic substructures. It investigates lineability issues in a variety of areas, including real and complex analysis. After presenting basic concepts about the existence of linear structures, the book discusses lineability properties of families of functions defined on a subset of the real line as well as the lineability of special families of holomorphic (or analytic) functions defined on some domain of the complex plane. It next focuses on spaces of sequences and spaces of integrable functions before covering the phenomenon of universality from an algebraic point of view. The authors then describe the linear structure of the set of zeros of a polynomial defined on a real or complex Banach space and explore specialized topics, such as the lineability of various families of vectors. The book concludes with an account of general techniques for discovering lineability in its diverse degrees.

This study in combinatorial group theory introduces the concept of automatic groups. It contains a succinct introduction to the theory of regular languages, a discussion of related topics in combinatorial group theory, and the connections between automatic groups and geometry which motivated the development of this new theory. It is of interest to mathematicians and computer scientists, and includes open problems that will dominate the research for years to come.

The selected contributions in this volume originated at the Sundance conference, which was devoted to discussions of current work in the area of free resolutions. The papers include new research, not otherwise published, and expositions that develop current problems likely to influence future developments in the field.

Examines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.

The book reports a comparative research project about algebra teaching and learning in four countries. Algebra is a central topic of learning across the world, and it is well-known that it represents a hurdle for many students. The book presents analyses built on extensive video-recordings of classrooms documenting the first introduction to symbolic algebra (students aged 12 to 14). While the content addressed in all classrooms is variables, expressions and equations, the teaching approaches are diverse. The chapters bring the reader into different algebra classrooms, discussing issues such as mathematization and social norms, the role of mediating tools and designed examples, and teacher beliefs. By comparing classrooms, new insights are generated about how students understand the algebraic content, how teachers instruct, and how both parties deal with difficulties in learning elementary algebra. The book also describes a research methodology using video in search of taken-for-granted aspects of algebra lessons.

This self-contained reference/text presents a thorough account of the theory of real function algebras. Employing the intrinsic approach, avoiding the complexification technique, and generalizing the theory of complex function algebras, this single-source volume includes: an introduction to real Banach algebras; various generalizations of the Stone-Weierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and a detailed bibliography.;Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f(2), Re f(3), and Re f(4); and the positivity of the real part of a linear functional on a subspace of C(X).;With over 600 display equations, this reference is for mathematical analysts; pure, applied, and industrial mathematicians; and theoretical physicists; and a text for courses in Banach algebras and function algebras.

This practical reference and text presents the applications of tensors, Lie groups and algebra to Maxwell, Klein-Gordon and Dirac equations, making elementary theoretical physics comprehensible and high-level theoretical physics accessible.;Providing the fundamental mathematics necessary to understand the applications, Tensors and the Clifford Algebra offers lucid discussions of covariant tensor calculus; examines subjects from a variety of perspectives; supplies highly detailed developments of all calculations; employs the language of physics in its explanations; and illustrates the use of Clifford algebra and tensor calculus in studying bosons and fermions.;With over 2800 display equations and 14 appendixes, this book should be a useful reference for mathematical physicists and applied mathematicians, and an important text for upper-level undergraduate and graduate students in quantum mechanics, relativity, electromagnetism, theoretical physics, elasticity and field theory courses.

Although there are many types of ring extensions, simple extensions have yet to be thoroughly explored in one book. Covering an understudied aspect of commutative algebra, Simple Extensions with the Minimum Degree Relations of Integral Domains presents a comprehensive treatment of various simple extensions and their properties. In particular, it examines several properties of simple ring extensions of Noetherian integral domains. As experts who have been studying this field for over a decade, the authors present many arguments that they have developed themselves, mainly exploring anti-integral, super-primitive, and ultra-primitive extensions. Within this framework, they study certain properties, such as flatness, integrality, and unramifiedness. Some of the topics discussed include Sharma polynomials, vanishing points, Noetherian domains, denominator ideals, unit groups, and polynomial rings. Presenting a complete treatment of each topic, Simple Extensions with the Minimum Degree Relations of Integral Domains serves as an ideal resource for graduate students and researchers involved in the area of commutative algebra.

This book is a collection of research papers and surveys on algebra that were presented at the Conference on Groups, Rings, and Group Rings held in Ubatuba, Brazil. This text familiarizes researchers with the latest topics, techniques, and methodologies in several branches of contemporary algebra. With extensive coverage, it examines broad themes from group theory and ring theory, exploring their relationship with other branches of algebra including actions of Hopf algebras, groups of units of group rings, combinatorics of Young diagrams, polynomial identities, growth of algebras, and more. Featuring international contributions, this book is ideal for mathematicians specializing in these areas.

For courses in Basic Mathematics. The Martin-Gay principle: Every student can succeed Elayn Martin-Gay's student-centric approach is woven seamlessly throughout her texts and MyLab courses, giving students the optimal amount of support through effective video resources, an accessible writing style, and study skills support built into the program. Elayn's legacy of innovations that support student success include Chapter Test Prep videos and a Video Organizer note-taking guide. Expanded resources in the latest revision bring even more updates to her program, all shaped by her focus on the student - a perspective that has made her course materials beloved by students and instructors alike. The Martin-Gay series offers market-leading content written by a preeminent author-educator, tightly integrated with the #1 choice in digital learning: MyLab Math. Also available with MyLab Math By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Bringing Elayn Martin-Gay's voice and approach into the MyLab course - though video resources, study skills support, and exercises refined with each edition - gives students the support to be successful in math. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0135161401 / 9780135161401 Basic College Mathematics Plus MyLab Math with Pearson eText -- Access Card Package, 6/e Package consists of: 0134840429 / 9780134840420 Basic College Mathematics 0135115787 / 9780135115787 MyLab Math with Pearson eText - Standalone Access Card - for Basic College Mathematics